Question

8.

If a principal of $2500 was invested at a rate of 5% compounded semiannually and terminates
with a balance of $5509.39, how long was the money invested for? hint: use table A11 or log calculations

4 yrs

8 yrs

16 yrs

32 yrs

Answer 1

The money was invested for 16 years

Explanation:

This is a compound interest problem and the following information has been provided;

Principal, P = 2500

Rate, r = 0.05 compounded semiannually. This will imply an effective rate of 0.05/2 = 0.025 effective per semiannual period.

Accumulated amount, A = 5509.39

We are required to determine the duration of investment in years. We let the number of years be n. We then use the compound interest formula;

`A=P(1+r)^(n)\\\\5509.39=2500(1+0.025)^(2n)`

We raise to power 2n since there are 2n semiannual periods in n years. The next step is to divide both sides by 2500;

`2.203756=1.025^(2n)\\`

We introduce logs in order to solve for n;

`ln(2.203756)=2nln(1.025)\\\\2n=(ln(2.203756))/(ln(1.025))\\ \\2n=32\\\\n=16`